Question

A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 106.9​,and the sample standard deviation is found to be 15.1. Is the population mean greater than 100 at the α=0.025 level of​ significance?

A) Determine the null and alternative hypotheses.

B) Compute the test statistic

C) Determine the​ P-value. ​(Round to three decimal places as​ needed.)

D) What is the result of the hypothesis​ test?

____ the null hypothesis because the​ P-value is _____ the level of significance. At the α=0.025 level of​ significance, the population mean ___

greater than 100.

less than 100.

different from 100.

greater than 100.

less than 106.9.

different from 106.9.

greater than 106.9.

Answer 1

Page No. Date solution! Given that, x = 106.9 6 - 15.1 n = 40 1 =100 2 -0.025 Hoil = 100 Hau 100 - 2 Test statistic, - x-u Z = 106.9-100 15.1/JGO z = 2.89 The test statistic is - 2.89 re? This is right -tailed test P(Z > 2.89) El-P (232.89) - - 0.998) 20.0019 P-value = 0.0 ola 0.0019 so.025 P-value za Reject Ho.

Page No. Data 1o Reject null hypthesis because the p-value is 0.0019 the level of significance. At the L = 0.025 level of significance, the population mean is greater than 100.